"Notre" acts as an adjective: "notre maison" = 'our house'; "nôtre" is a stand-alone pronoun, it replaces the noun: "cette maison est la nôtre" = 'this house is ours'.
Hi philmorse, I found choracaraco’s comment helpful:
"Notre" acts as an adjective: "notre maison" = 'our house'; "nôtre" is a stand-alone pronoun, it replaces the noun: "cette maison est la nôtre" = 'this house is ours'.